Bill Belichick has a bit of a problem as he heads into the 2014 offseason.

“When your season goes into the postseason as ours did for three weeks, you’re behind going into the college draft and to a certain degree, I would say the free agency process,” Belichick said. “So we have some catching up to do.”

Fortunately, Bill, we’re here to help. The Patriots had a nice season in 2013 — winning 12 games in the regular season, reaching the AFC Championship game — but the roster needs some serious retooling, particularly on offense, where they need to upgrade the skill positions to get the most out of the remaining years of Tom Brady.

The Patriots have a little bit of time to get their house in order — free agency begins March 11 and the draft is in early May — but before that, they have to work on their salary cap situation.

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The Patriots don’t have a ton of cap space; they have approximately $123 million committed to the top 51 contracts for 2014, with the salary cap presumed to be around $125 million (plus an extra $5 million they can roll over from this year).

The key could be whether the Patriots get a partial or full cap refund on Aaron Hernandez, who currently counts $7.5 million against the 2014 cap, although it doesn’t seem likely that the situation will be resolved before free agency begins.

The Patriots need more flexibility before March 11, and it can be achieved if they make some decisions that could be emotionally difficult but make all kinds of financial sense.

The most difficult — but also obvious — move is to restructure the contract of Wilfork, who is entering the final season of his deal and has a salary cap number of $11.6 million. Wilfork is the heart and soul of this team, but that number is much too high given his age (33 next fall), position (a run-stuffing defensive tackle isn’t as crucial as it used to be), and because the Patriots went 12-4 without him for most of the season.

Elise Amendola/AP

The Patriots still won 12 games while playing with Vince Wilfork on the sideline for most of the season.

The Patriots could save $8 million against the cap by outright cutting him, but realistically, they should look to extend his contract by five years (for signing-bonus proration purposes) and get his cap number in the $4 million-$5 million range for next year.

Connolly, who will be 32 in the fall, had an average-to-subpar season at right guard, and his $4.083 million cap number is out of line with his level of play. He is entering the final year of his contract, and they can create $3 million in cap space by outright cutting him. At minimum they should look to restructure and extend his contract.

Gostkowski is also entering the final year of his contract. He shouldn’t go anywhere — he’s one of the best four or five kickers in the league — and the Patriots should look to sign him to an extension to lower his $3.8 million cap number for this year.

2. Re-sign Julian Edelman and sign at least one other wide receiver.

The shame of this season was that Brady, who will turn 37 in August, didn’t have much depth at the skill positions, especially when Rob Gronkowski was out. The Patriots’ window with Brady is closing, and they need to surround him with better talent, pronto.

Barry Chin/Globe Staff

Will Julian Edelman be back to catch passes from Tom Brady?

That’s why they should look to upgrade Brady’s weapons through free agency. There is no more time to be developing kids, as they did with Aaron Dobson, Kenbrell Thompkins, and Josh Boyce. Dobson showed some potential, but he should enter next season as the No. 4 receiver, not No. 2.

The Patriots need finished products. A few intriguing names that could be available: Hakeem Nicks, Kenny Britt (a Rutgers connection), Eric Decker, and James Jones, and all but Decker could likely be a relative bargain.

Edelman is a must-sign after proving his toughness, durability, and skill as a receiver, and his elite abilities as a punt returner.

The Patriots didn’t get a chance to replace Hernandez since he was arrested and kicked off the team in July, well after the draft and free agency period. And finding at least one tight end is imperative now that the injuries are starting to add up with Gronkowski, who is an All Pro when he’s on the field but can’t seem to stay healthy.

Kevin C. Cox/Getty Images

Tony Gonzalez said he would retire, but could he be enticed to play another year with the Patriots?

A few decent veterans could be available in free agency — Brandon Pettigrew and Scott Chandler among them — but in our view, the perfect addition would be Gonzalez, the 14-time Pro Bowler.

Yes, he will soon be 38, but he caught 83 passes for 859 yards and eight touchdowns this year and clearly has gas left in the tank. A combination of Gonzalez and Gronkowski would be absolutely devastating, and he would be a great veteran addition to the locker room.

Gonzalez has said he will retire after this season, but he never reached a Super Bowl, so let’s see how he feels in August when training camps start heating up. Belichick should tell Gonzalez he can train on his own in the offseason, and show up to training camp in the third week of August. You make special rules to bring in a player of Gonzalez’s caliber.

4. Franchise Aqib Talib.

It would cost the Patriots around $11 million to tag Talib for the 2014 season, but that seems to be the most rational approach, especially if they can create cap space with Wilfork, Connolly, Gostkowski, and perhaps Hernandez.

Talib is coming off an excellent season, and has elite measurables that allow the Patriots to be much more versatile on defense. But his past is checkered enough that the Patriots shouldn’t give him a $20 million signing bonus or a long-term contract that could come back to bite them in two or three years.

5. Sign a veteran defensive lineman.

Rob Ninkovich and Chandler Jones seemed to hit a wall, as they played more than 95 percent of the snaps this season. Three veteran pass rushers that would look good in a Patriots uniform might get to free agency: Cincinnati’s Michael Johnson, the Giants’ Justin Tuck, and Denver’s Shaun Phillips.

And the Patriots could use more depth at defensive tackle, especially with Wilfork and Tommy Kelly both on the wrong side of 30. Jones’s brother, the Ravens’ Arthur Jones, would be a good versatile piece who could play tackle or end. And the Dolphins’ Randy Starks, whom Belichick has faced twice per year since 2008, is still an excellent interior player who seemingly wants out of Miami.

6. Take offensive linemen and the best available defensive players in the draft.

The Patriots need upgrades at right guard and center, and that can easily be done with a mid-to-high draft pick (they select 29th in the first round). On defense, they have a solid core of young players — Jones, Dont’a Hightower, Alfonzo Dennard, Devin McCourty, Jamie Collins, Logan Ryan — and should continue to supplement it with young pass rushers, linebackers, and defensive backs. If they don’t sign a tight end or receiver in free agency, then drafting one with a high pick becomes imperative.

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